n-widths of Sobolev spaces in \(L^ p\)
Let \(W_ p^{(r)}=\{f: f\in C^{r-1}[0,1]\), \(f^{(r-1)}\) abs. cont., \(\| f^{(r)}\|_ p<\infty \}\), and set \(B_ p^{(r)}=\{f: f\in W_ p^{(r)}\), \(\| f^{(r)}\|_ p\leq 1\}\). We find the exact Kolmogorov, Gel'fand, linear, and Bernstein n-widths of \(B_ p^{(r)}\) in \(L^ p\) for all \(p\in (1,\infty)\). For the Kolmogorov n-width we show that for \(n\geq r\) there exists an optimal subspace of splines of degree r-1 with n-r fixed simple knots depending on p.
scientific article; zbMATH DE number 3931653